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\newtheorem{theorem}{Theorem}
\newtheorem{acknowledgement}[theorem]{Acknowledgement}
\newtheorem{algorithm}[theorem]{Algorithm}
\newtheorem{axiom}[theorem]{Axiom}
\newtheorem{case}[theorem]{Case}
\newtheorem{claim}[theorem]{Claim}
\newtheorem{conclusion}[theorem]{Conclusion}
\newtheorem{condition}[theorem]{Condition}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{criterion}[theorem]{Criterion}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}
\newtheorem{exercise}[theorem]{Exercise}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{notation}[theorem]{Notation}
\newtheorem{problem}[theorem]{Problem}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{solution}[theorem]{Solution}
\newtheorem{summary}[theorem]{Summary}
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\begin{document}
Al desarrollar la expresi\'{o}n $\left(  \dfrac{1}{16}x+3y\right)  \left(
x-4y\right)  ^{2}$ se obtiene:\newline\qquad a) $\frac{1}{16}x^{3}+\frac{5}%
{2}x^{2}y-23xy^{2}+48y^{3}\qquad$b) $\frac{1}{16}x^{3}+\frac{5}{2}%
x^{2}y-23xy^{2}+24y^{3}\medskip$\newline\qquad c)$\frac{1}{16}x^{3}+\frac
{5}{2}x^{2}y^{2}-23xy^{2}+48y^{3}\qquad$d) $\frac{1}{16}x^{3}+\frac{5}{4}%
x^{2}y-23xy^{2}+48y^{3}$

Al desarrollar la expresi\'{o}n $\left(  \dfrac{7}{16}x+3y\right)  \left(
x-\dfrac{1}{2}y\right)  ^{2}$ se obtiene:\newline\qquad a) $\frac{7}{16}%
x^{3}+\frac{41}{16}x^{2}y-\frac{185}{64}xy^{2}+\frac{3}{4}y^{3}\qquad$b)
$\frac{7}{16}x^{3}+\frac{41}{16}x^{2}y-\frac{185}{64}xy^{2}+y^{3}\medskip
$\newline\qquad c) $\frac{7}{16}x^{3}+\frac{41}{16}x^{2}y^{2}-\frac{185}%
{64}xy^{2}+\frac{3}{4}y^{3}\qquad$d) $\frac{7}{16}x^{3}+\frac{41}{10}%
x^{2}y-\frac{185}{64}xy^{2}+\frac{3}{4}y^{3}$

Al desarrollar la expresi\'{o}n $\left(  2x+3y\right)  \left(  7x-y\right)
^{2}$ se obtiene:\newline\qquad a) $98x^{3}+119x^{2}y-40xy^{2}+3y^{3}\qquad$b)
$98x^{3}+117x^{2}y-40xy^{2}+3y^{3}\medskip$\newline\qquad c) $93x^{3}%
+119x^{2}y-40xy^{2}+3y^{3}\qquad$d) $98x^{3}+119x^{2}y-4xy^{2}+3y^{3}$

Al desarrollar la expresi\'{o}n $\left(  5x+y\right)  \left(  7x-2y\right)
^{2}$ se obtiene:\newline\qquad a) $245x^{3}-91x^{2}y-8xy^{2}+4y^{3}\qquad$b)
$245x^{3}-89x^{2}y-8xy^{2}+4y^{3}\medskip$\newline\qquad c) $245x^{3}%
-91x^{2}y-8x^{2}y^{2}+4y^{3}\qquad$d) $245x^{3}-91x^{2}y^{2}-8xy^{2}+4y^{3}$

Al desarrollar la expresi\'{o}n $\left(  \dfrac{3}{2}x+\dfrac{1}{7}y\right)
\left(  x-2y\right)  ^{2}$ se obtiene:\newline\qquad a) $\frac{3}{2}%
x^{3}-\frac{41}{7}x^{2}y+\frac{38}{7}xy^{2}+\frac{4}{7}y^{3}\qquad$b)
$\frac{3}{2}x^{3}-\frac{41}{7}x^{2}y+\frac{28}{7}xy^{2}+\frac{4}{7}%
y^{3}\medskip$\newline\qquad c) $\frac{3}{2}x^{3}-\frac{41}{7}x^{2}y+\frac
{38}{7}xy^{2}+\frac{1}{7}y^{3}\qquad$d) $\frac{3}{2}x^{3}-\frac{24}{7}%
x^{2}y+\frac{38}{7}xy^{2}+\frac{4}{7}y^{3}$

Al desarrollar la expresi\'{o}n $\left(  5x+3y\right)  \left(  6x-y\right)
^{2}$ se obtiene:\newline\qquad\medskip a) $180x^{3}+48x^{2}y-31xy^{2}+3y^{3}%
$\qquad b) $180x^{3}+48x^{2}y^{2}+31xy^{2}+3y^{3}$\newline\qquad c)
$180x^{3}+48x^{2}y-31xy+3y^{3}$\qquad d) $180x^{3}+48x^{2}y+31xy^{2}+3y^{3}$

Al desarrollar la expresi\'{o}n $\left(  2x+y\right)  \left(  6x-3y\right)
^{2}$ se obtiene:\newline\qquad a) $72x^{3}-36x^{2}y-18xy^{2}+9y^{3}$\qquad b)
$72x^{3}-36xy^{2}-18x^{2}y+9y^{3}$\medskip\newline\qquad c) $72x^{3}%
-36x^{2}y-18xy+9y^{3}$\qquad d) $72x^{3}-33x^{2}y+18xy^{2}+9y^{3}$

Al desarrollar la expresi\'{o}n $\left(  2x-7y\right)  \left(  9x+y\right)
^{2}$ se obtiene:\newline\qquad\medskip a) $162x^{3}-531x^{2}y-124xy^{2}%
-7y^{3}$\qquad b) $162x^{3}-530x^{2}y-124xy^{2}-7y^{3}$\newline\qquad c)
$162x^{3}-531xy^{2}-124xy-7y^{3}$\qquad d) $162x^{3}-531x^{2}y^{2}%
-124xy^{2}-7y^{3}$

Al desarrollar la expresi\'{o}n $\left(  5x-y\right)  \left(  5x+3y\right)
^{2}$ se obtiene:\newline\qquad\medskip a) $175x^{3}+185x^{2}y+33xy^{2}%
-9y^{3}$\qquad b) $175x^{3}+182x^{2}y-33xy^{2}-9y^{3}$\newline\qquad c)
$175x^{3}+185x^{2}y^{2}+33xy-9y^{3}$\qquad d) $175x^{3}+185xy^{2}%
+33x^{2}y-9y^{3}$

Al desarrollar la expresi\'{o}n $\left(  x-7y\right)  \left(  9x-2y\right)
^{2}$ se obtiene:\newline\qquad\medskip a) $81x^{3}-603x^{2}y+256xy^{2}%
-28y^{3}$\qquad b) $81x^{3}-603x^{2}y^{2}+256xy-28y^{3}$\newline\qquad c)
$81x^{3}-600x^{2}y+256xy-28y^{3}$\qquad d) $81x^{3}-603x^{2}y^{2}%
-256xy^{2}-28y^{3}$

Al desarrollar la expresi\'{o}n $\left(  5x-3y\right)  \left(  7x-2y\right)
^{2}$ se obtiene:\newline\qquad\medskip a) $245x^{3}-287x^{2}y+104xy^{2}%
-12y^{3}$\qquad b) $245x^{3}-287x^{2}y^{2}+104xy^{2}-12y^{3}$\newline\qquad c)
$245x^{3}-280x^{2}y+104xy^{2}-12y^{3}$\qquad d) $245x^{3}+287x^{2}%
y^{2}+104xy^{2}-12y^{3}$

Al desarrollar la expresi\'{o}n $\left(  3x-y\right)  \left(  5x-2y\right)
^{2}$ se obtiene:\newline\qquad\medskip a) $75x^{3}-85x^{2}y+32xy^{2}-4y^{3}%
$\qquad b) $75x^{3}-80x^{2}y^{2}+32xy^{2}-4y^{3}$\newline\qquad c)
$75x^{3}+85x^{2}y^{2}+32xy-4y^{3}$\qquad d) $75x^{3}-85x^{2}y+32xy-4y^{3}$

Al desarrollar la expresi\'{o}n $\left(  2x+3y\right)  \left(  5x-y\right)
^{2}$ se obtiene:\newline\qquad a) $50x^{3}+55x^{2}y-28xy^{2}+3y^{3}$\qquad b)
$50x^{3}+50x^{2}y^{2}-28xy^{2}+3y^{3}$\medskip\qquad\newline\qquad c)
$50x^{3}+50x^{2}y-28xy^{2}+3y^{3}$\qquad d) $50x^{3}+55x^{2}y-28xy+3y^{3}$

Al desarrollar la expresi\'{o}n $\left(  x-5y\right)  \left(  7x+3y\right)
^{2}$ se obtiene:\newline\qquad\medskip a) $49x^{3}-203x^{2}y-201xy^{2}%
-45y^{3}$\qquad b) $49x^{3}-203x^{2}y-201xy^{2}-45y^{3}$\qquad\newline\qquad
c) $49x^{3}-203x^{2}y-201xy^{2}-45y^{3}$\qquad d) $49x^{3}-203x^{2}%
y-201xy^{2}-45y^{3}$

Al desarrollar la expresi\'{o}n $\left(  7x+2y\right)  \left(  3x-y\right)
^{2}$ se obtiene:\newline\qquad\medskip a) $63x^{3}-24x^{2}y-5xy^{2}+2y^{3}%
$\qquad b)$63x^{3}-22x^{2}y-5xy^{2}+2y^{3}$\newline\qquad c) $63x^{3}%
-22x^{2}y-5xy+2y^{3}$\qquad d) $63x^{3}-24x^{2}y^{2}-5xy^{2}+2y^{3}$


\end{document}